POSSIBILITIES OF ARTIFICIAL INTELLIGENCE IN TEACHING HIGHER MATHEMATICS

Abstract

The example of application of methods of computer representation of knowledge to the «Matrix» of the higher mathematics course, the authors examine the possibility of using elements of artificial intelligence, but do not propose an exhaustive algorithm for the construction of relevant systems, and based on the known thesis: «intellectual tasks no formal solution algorithm». Moreover, we implicitly proceed from the concept that when solving problems that require the participation of human intelligence, artificial intelligence can be only an auxiliary tool. Analysis of Russian and English sources has led to the conclusion that automated the process of proving mathematical theorems with the use of artificial intelligence (including neural networks) leads first-year students does not lead first-year students to the natural goal of teaching higher mathematics – » to teach logical reasoning. Usually the result comes down to «programmed» using the keyboard that, in certain circumstances, of course, is a very useful skill. But, unfortunately, the task «to teach the student to think, to reason logically and think outside the box», based on modern level of development of artificial intelligence (machine learning), according to the authors, is not yet resolved. Using the same knowledge base in an adequate format, and semantic networks allow at least allow you to at least get closer to the possibility of using artificial intelligence in the proof of theorems of higher mathematics. Because properly constructed semantic network will greatly assist as a teacher is in presenting the proof of the theorem, and demonstrate to the students a well-known logical connections and, we hope, will interest them in creating a new one. The above arguments determine the purpose of the proposed study is to build semantic networks for proof of mathematical theorems, and to solve the so-called «proof-based» tasks. In our opinion, the results of this study will not only contribute to streamlining the structure by the teacher and better understanding by students of the relevant sections of mathematics, but few will bring the solution of the problem of formation of artificial intelligence, based on the decision of «evidence-based» tasks of higher mathematics.